Lectures Advanced Research Methods and Statistics for Psychology (ARMS)
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What determines whether the patient is diagnosed?
Sensitivity: how far are these curves apart? How good can. the participant discriminate between these two curves?
There is also a criterion:
Everything > the criterion: we say that the signal is present.
Everything < the criterion: the signal is not present.
This can also be presented as:
From the data from an experiment you could tell how many hits, false alarms, misses and correct rejections there were; you make the decision matrix.
To calculate sensitivity, you only need hits and false alarms. You can calculate this in excel using:
Hits: =IF(AND(CEL=1,CEL=1),1,0)
False alarm: =IF(AND(CEL=0,CEL=1),1,0)
Then you calculate the sum of hits and false alarms, and then you can fill in the matrix.
Amount of misses: (Total amount of stimuli-present trials) - hits
Amount of correct rejections: (Total amount of stimuli-non-present trials) - false alarms
From your raw data, your matrix might look like this:
For the decision matrix, you divide everything by the total number:
To calculate sensitivity, we use d’ (d-prime). d’ = how many standard deviations are the mean of the signal and the mean of the noise apart? d’ = 1 stdev, d’ = 2 stdev etc. The smaller the d’, the lower the sensitivity. We calculate this using:
Reasoning: the difference between the means = the difference between the distance to criterium.
To calculate the Z in excel: normsinv(proportion hits or false alarms). So the total formula to calculate d’: normsinv(hits) – normsinv(false alarms). You use the rates for this formula, not the amounts.
You get a negative d’ if the person was worse than 50% chance of getting it right; they can do this purposefully or maybe they didn’t read the instructions well. This person is still sensitive
In summary, the steps for computing d’:
Every person has a criterion. The criterion can change by e.g. change in the instructions to the participant.
There are two measures for criterion: C=criterion, beta=bias.
You calculate criterion using:
If the criterion is 0, the person has no bias to right or left: it’s placed in the middle of the two curves.
Negative criterion: tendency to say ‘yes, there is a target’
Positive criterion: tendency to say ‘no’
You calculate beta using:
Beta < 1 : tendency to say yes
Beta = 1 : no bias
Beta > 1 : tendency to say no
Tendency to say no: More misses, few FA C> 0 Beta > 1 |
Tendency to say yes: Few misses, more FA C< 0 Beta < 1 |
d’ and the criterion are independent.
With the ROC-curve you combine the d’ and criterion:
This person is just guessing.
There are two assumptions for computing d’ and C:
This is violated whwn the sensitivity (d’) and the criterium are not independent: the d’ differs for different criteria.
Examples of causes for violation:
Consequences of violation:
You can still calculate the AUC/A’; the area under the curve.
How to check? Look at the ROC curve for multiple criteria:
How to calculate AUC? You can use excel for this:
First rank the proportions! Highest numbers on top.
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In this bundle you can find the lecture and seminar notes for the course 'Advanced Research Methods and Statistics for Psychology (ARMS)'. I followed this course on Utrecht University, during the bachelor (neuro)psychology.
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